Mugunghwa(also known as Hibiscus syriacus and rose of Sharon) is the national flower of Korea because it represents determination, politeness, and endurance and also expresses Koreans' feelings in the best way.

Mugunghwa Festival at Gwanghwamun Square

In the 880AD, China called the country of "mugunghwa", which means "the flower that never faded" in Korean, to the old dynasty of Korea. 
At the same time, Aegeukga (the song of patriotism), which is considered the national anthem of the country with the proclamation of the Republic of Korea on August 15, 1948, contains the words "three thousand magnificent mountains filled with Mugunghwa and rivers". 
Mugunghwa is a symbol in the flags of government, and a pattern in the emblem of the National Assembly.
Source: The Book named "The Reality of Korea: The Past and Present of Korea" - Korean Culture and Information Service, The Book named "National Symbols of the Republic of Korea"